Senate leaders are meeting Sunday to find a way out the government shutdown and the threat of a first-ever US debt default. They're searching for an end to a political crisis that has stalled all other legislative business while driving public opinion of Congress to new lows.

Senate Majority Leader Sen. Harry Reid pauses as Sen. Chuck Schumer speaks during a news conference Saturday. The federal government remains partially shut down and faces a first-ever default between Oct. 17 and the end of the month.

As two political clocks tick in opposite directions in Washington – the one counting the partial government shutdown, now in its 13th day, and the other noting just four days until the Treasury Department says the US could default on its debt – all eyes are on the US Senate.

“The World’s Greatest Deliberative Body,” as it has been called, was in unusual Sunday session, Speaker John Boehner having given up for now and sent House members home for the weekend.

In the Senate on Saturday, Democrats couldn’t generate the 60 votes necessary to bring Majority Leader Harry Reid’s proposal to the floor. That would have extended the debt ceiling through 2014. It failed on a party line vote.

For a while, it looked like a bipartisan proposal by Sen. Susan Collins, the moderate Republican from Maine, might be going somewhere. That included a six-month stopgap funding bill through March and a debt ceiling increase through January.

Regarding the Affordable Care Act (“Obamacare”), the Collins proposal also would delay for two years a tax on medical devices, and it included stronger income verification for those deemed eligible for insurance subsidies under the new law.

Democrats saw that as merely delaying the debt ceiling fight for three months, and they rejected it. But the Collins proposal – at least its major elements – remained a point of discussion as Reid, McConnell, and their top lieutenants reconvened Sunday.

Whatever they eventually come up with – which will then have to be considered by the more-fractious House as the Oct. 17 debt ceiling deadline moves inexorably closer – undoubtedly will impact public opinion moving toward the 2014 mid-term elections.

Historically, job security for lawmakers is unusually high – unusual given the low opinion in which their institution itself is held.

“In 2012, Congressional approval averaged 15 percent, the lowest in nearly four decades of Gallup polling,” Washington Post political blogger Chris Cillizza noted earlier this year. “And yet, 90 percent of House Members and 91 percent of Senators who sought re-election won last November.”

Could that change in 2014? Gerrymandering, changes in election and campaign law (voting rights and money), and outside influences (money again, plus the tea party) make that hard to answer with any certainty.

And yet a new HuffPost/YouGov poll should be making lawmakers nervous.

“Do you think most members of Congress deserve to be reelected, or not?” 1,000 US adults were asked. Seventy percent said “no,” and only 11 percent said “yes.”

More to the point, only 25 percent said “yes” when asked, “Do you think the member of Congress from your congressional district deserves to be reelected, or not?” Nearly twice as many (47 percent) said “no.”

Other recent polls had similar results.

AN Associated Press-GfK survey this past week found that “Congress is scraping rock bottom, with a ghastly approval rating of 5 percent.”

“Indeed, anyone making headlines in the dispute has earned poor marks for his or her trouble, whether it's Democrat Harry Reid, the Senate majority leader, or Republican John Boehner, the House speaker, both with a favorability rating of 18 percent,” the AP reported.

“While senators are in Washington, their days are scheduled in fifteen-minute intervals: staff meetings, interviews, visits from lobbyists and home-state groups, caucus lunches, committee hearings, briefing books, floor votes, fund-raisers. Each senator sits on three or four committees and even more subcommittees, most of which meet during the same morning hours, which helps explain why committee tables are often nearly empty, and why senators drifting into a hearing can barely sustain a coherent line of questioning. All this activity is crammed into a three-day week, for it’s an unwritten rule of the modern Senate that votes are almost never scheduled for Mondays or Fridays, which allows senators to spend four days away from the capital.”

That’s the backdrop against which Reid and McConnell are trying to extricate themselves – and the country – from the current political mess.